The representation of an inventory as a list of symbols or a list of prices
is naive. A sales clerk in a toy store not only needs to know the name of
the toy, but also its price, and possibly other attributes like warehouse
availability, delivery time, or even a picture. Similarly, representing a
company's personnel as a list of hours is a bad choice. Even the printing
of a paycheck requires more information about the employee than the hours
worked per week.
Fortunately, the items of lists do not have to be atomic values. Lists may
contain whatever values we want, especially structures. Let's try to make
our toy store inventory functions more realistic. We start with the
structure and the data definition of a class of inventory records:
<#11496#>(define-struct<#11496#> <#11497#>ir<#11497#> <#11498#>(name<#11498#> <#11499#>price))<#11499#>
An <#62412#><#11504#>inventory record<#11504#><#62412#> (<#62413#><#11505#>ir<#11505#><#62413#>) is a structure:
<#70982#> <#62414#><#11506#>(make-ir<#11506#>\ <#11507#>s<#11507#>\ <#11508#>n)<#11508#><#62414#> <#70982#>
where <#62415#><#11509#>s<#11509#><#62415#> is a symbol and <#62416#><#11510#>n<#11510#><#62416#> is a (positive) number.
Most importantly, we can define a class of lists that represent
an inventory much more realistically:
An <#62417#><#11513#>inventory<#11513#><#62417#> is either
- <#62418#><#11515#>empty<#11515#><#62418#> or
- <#62419#><#11516#>(cons<#11516#>\ <#11517#>ir<#11517#>\ <#11518#>inv)<#11518#><#62419#>
where <#62420#><#11519#>ir<#11519#><#62420#> is an inventory record and <#62421#><#11520#>inv<#11520#><#62421#> is an inventory.
While the shape of the list definition is the same as before, its
components are defined in a separate data definition. Since this is our
first such data definition, we should make up some examples before we
proceed.
The simplest example of an inventory is <#62422#><#11523#>empty<#11523#><#62422#>. To
create a larger inventory, we must create an inventory record and
<#62423#><#11524#>cons<#11524#><#62423#> it onto another inventory:
<#11529#>(c<#11529#><#11530#>ons<#11530#> <#11531#>(make-ir<#11531#> <#11532#>'<#11532#><#11533#>doll<#11533#> <#11534#>17.95)<#11534#>
<#11535#>empty)<#11535#>
From here, we can create yet a larger inventory listing:
<#11543#>(c<#11543#><#11544#>ons<#11544#> <#11545#>(make-ir<#11545#> <#11546#>'<#11546#><#11547#>robot<#11547#> <#11548#>22.05)<#11548#>
<#11549#>(c<#11549#><#11550#>ons<#11550#> <#11551#>(make-ir<#11551#> <#11552#>'<#11552#><#11553#>doll<#11553#> <#11554#>17.95)<#11554#>
<#11555#>empty))<#11555#>
Now we can adapt our inventory-processing functions. First look at
<#62424#><#11559#>sum<#11559#><#62424#>, the function that consumes an inventory and produces its total
value. Here is a re-statement of the basic information about the function:
<#70983#>;; <#62425#><#11564#>sum<#11564#> <#11565#>:<#11565#> <#11566#>inventory<#11566#> <#11567#><#11567#><#11568#>-;SPMgt;<#11568#><#11569#><#11569#> <#11570#>number<#11570#><#62425#><#70983#>
<#70984#>;; to compute the sum of prices on <#62426#><#11571#>an-inv<#11571#><#62426#><#70984#>
<#11572#>(define<#11572#> <#11573#>(sum<#11573#> <#11574#>an-inv)<#11574#> <#11575#>...)<#11575#>
For our three sample inventories, the function should produce the following
results: <#62427#><#11579#>0<#11579#><#62427#>, <#62428#><#11580#>17.95<#11580#><#62428#>, and <#62429#><#11581#>40.0<#11581#><#62429#>.
Since the data definition of inventories is basically that of lists, we can
again start from the template for list-processing functions:
<#11586#>(d<#11586#><#11587#>efine<#11587#> <#11588#>(sum<#11588#> <#11589#>an-inv)<#11589#>
<#11590#>(c<#11590#><#11591#>ond<#11591#>
<#11592#>[<#11592#><#11593#>(empty?<#11593#> <#11594#>an-inv)<#11594#> <#11595#>...]<#11595#>
<#11596#>[<#11596#><#11597#>else<#11597#> <#11598#>...<#11598#> <#11599#>(first<#11599#> <#11600#>an-inv)<#11600#> <#11601#>...<#11601#> <#11602#>(sum<#11602#> <#11603#>(rest<#11603#> <#11604#>an-inv))<#11604#> <#11605#>...]<#11605#><#11606#>))<#11606#>
Following our recipe, the template only reflects the data definition of the
input, not that of its constituents. Therefore the template for <#62430#><#11610#>sum<#11610#><#62430#>
here is indistinguishable from that in section~#seclistsmore#11611>.
For the definition of the function body, we consider each <#62431#><#11612#>cond<#11612#><#62431#>-line
in isolation. First, if <#62432#><#11613#>(empty?<#11613#>\ <#11614#>an-inv)<#11614#><#62432#> is true, <#62433#><#11615#>sum<#11615#><#62433#> is
supposed to produce <#62434#><#11616#>0<#11616#><#62434#>. Hence, the answer expression in the first
<#62435#><#11617#>cond<#11617#><#62435#>-line is obviously <#62436#><#11618#>0<#11618#><#62436#>.
<#11623#>(d<#11623#><#11624#>efine<#11624#> <#11625#>(sum<#11625#> <#11626#>an-inv)<#11626#>
<#11627#>(c<#11627#><#11628#>ond<#11628#>
<#11629#>[<#11629#><#11630#>(empty?<#11630#> <#11631#>an-inv)<#11631#> <#11632#>0]<#11632#>
<#11633#>[<#11633#><#11634#>else<#11634#> <#11635#>(+<#11635#> <#11636#>(ir-price<#11636#> <#11637#>(first<#11637#> <#11638#>an-inv))<#11638#> <#11639#>(sum<#11639#> <#11640#>(rest<#11640#> <#11641#>an-inv)))]<#11641#><#11642#>))<#11642#>
<#11646#>Figure: Computing the value of an inventory<#11646#>
Second, if <#62437#><#11648#>(empty?<#11648#>\ <#11649#>an-inv)<#11649#><#62437#> is false, <#11650#>i.e.<#11650#>, <#62438#><#11651#>sum<#11651#><#62438#> is applied
to a <#62439#><#11652#>cons<#11652#><#62439#>tructed inventory, the recipe requires us to understand
the purpose of two expressions:
- <#62440#><#11654#>(first<#11654#>\ <#11655#>an-inv)<#11655#><#62440#>, which extracts the first item of the list; and
- <#62441#><#11656#>(sum<#11656#>\ <#11657#>(rest<#11657#>\ <#11658#>an-inv))<#11658#><#62441#>, which extracts the rest of
<#62442#><#11659#>an-inv<#11659#><#62442#> and then computes its cost with <#62443#><#11660#>sum<#11660#><#62443#>.
To compute the total cost of the entire input <#62444#><#11662#>an-inv<#11662#><#62444#> in the second
case, we must determine the cost of the first item. The cost of
the first item may be obtained via the selector <#62445#><#11663#>ir-price<#11663#><#62445#>, which
extracts the price from an inventory record. Now we just add the cost of
the first item and the cost of the rest of the inventory:
<#11668#>(+<#11668#> <#11669#>(ir-price<#11669#> <#11670#>(first<#11670#> <#11671#>an-inv))<#11671#>
<#11672#>(sum<#11672#> <#11673#>(rest<#11673#> <#11674#>an-inv)))<#11674#>
The complete function definition is contained in figure~#figsumir#11678>.
<#11681#>Exercise 10.2.1<#11681#>
Adapt the function <#62446#><#11683#>contains-doll?<#11683#><#62446#> so that it consumes inventories
instead of lists of symbols:
<#70985#>;; <#62447#><#11688#>contains-doll?<#11688#> <#11689#>:<#11689#> <#11690#>inventory<#11690#> <#11691#><#11691#><#11692#>-;SPMgt;<#11692#><#11693#><#11693#> <#11694#>boolean<#11694#><#62447#><#70985#>
<#70986#>;; to determine whether <#62448#><#11695#>an-inv<#11695#><#62448#> contains a record for <#62449#><#11696#>'<#11696#><#11697#>doll<#11697#><#62449#><#70986#>
<#11698#>(define<#11698#> <#11699#>(contains-doll?<#11699#> <#11700#>an-inv)<#11700#> <#11701#>...)<#11701#>
Also adapt the function <#62450#><#11705#>contains?<#11705#><#62450#>, which consumes a symbol and an
inventory and determines whether an inventory record with this symbol
occurs in the inventory:
<#70987#>;; <#62451#><#11710#>contains?<#11710#> <#11711#>:<#11711#> <#11712#>symbol<#11712#> <#11713#>inventory<#11713#> <#11714#><#11714#><#11715#>-;SPMgt;<#11715#><#11716#><#11716#> <#11717#>boolean<#11717#><#62451#><#70987#>
<#70988#>;; to determine whether <#62452#><#11718#>inventory<#11718#><#62452#> contains a record for <#62453#><#11719#>asymbol<#11719#><#62453#><#70988#>
<#11720#>(define<#11720#> <#11721#>(contains?<#11721#> <#11722#>asymbol<#11722#> <#11723#>an-inv)<#11723#> <#11724#>...)<#11724#>
Solution<#62454#><#62454#>
rawhtml20
<#11733#>Figure: A table of toys<#11733#>
<#11735#>Exercise 10.2.2<#11735#>
Provide a data definition and a structure definition for an inventory that
includes pictures with each objects. Show how to represent the inventory
listing in figure~#figtoytable#11737>.
Develop the function <#62455#><#11739#>show-picture<#11739#><#62455#>. The function consumes a symbol,
the name of a toy, and one of the new inventories. It produces the picture
of the named toy or <#62456#><#11740#>false<#11740#><#62456#> if the desired item is not in the
inventory. Pictures of toys are available on the Web.~ Solution<#62457#><#62457#>
<#11746#>Exercise 10.2.3<#11746#>
Develop the function <#62458#><#11748#>price-of<#11748#><#62458#>, which consumes the name of a toy and
an inventory and produces the toy's price.
Solution<#62459#><#62459#>
<#11754#>Exercise 10.2.4<#11754#>
A phone directory combines names with phone numbers. Develop a data
definition for phone records and directories. Using this data definition
develop the functions
- <#62460#><#11757#>whose-number<#11757#><#62460#>, which determines the name that goes with some
given phone number and phone directory, and
- <#62461#><#11758#>phone-number<#11758#><#62461#>, which determines the phone number that goes
with some given name and phone directory.
Solution<#62462#><#62462#>
Suppose a business wishes to separate all those items that sell for a
dollar or less from all others. The goal might be to sell these items in a
separate department of the store. To perform this split, the business also
needs a function that can extract these items from its inventory listing,
<#11767#>i.e.<#11767#>, a function that produces a list of structures.
Let us name the function <#62463#><#11768#>extract1<#11768#><#62463#> because it creates an inventory
from all those inventory records whose price item is less than or equal to
<#62464#><#11769#>1.00<#11769#><#62464#>. The function consumes an inventory and produces one with
items of appropriate prices. Thus the contract for <#62465#><#11770#>extract1<#11770#><#62465#> is
easy to formulate:
<#70989#>;; <#62466#><#11775#>extract1<#11775#> <#11776#>:<#11776#> <#11777#>inventory<#11777#> <#11778#><#11778#><#11779#>-;SPMgt;<#11779#><#11780#><#11780#> <#11781#>inventory<#11781#><#62466#><#70989#>
<#70990#>;; to create an <#62467#><#11782#>inventory<#11782#><#62467#> from <#62468#><#11783#>an-inv<#11783#><#62468#> for all<#70990#>
<#11784#>;; those items that cost less than $1<#11784#>
<#11785#>(define<#11785#> <#11786#>(extract1<#11786#> <#11787#>an-inv)<#11787#> <#11788#>...)<#11788#>
We can reuse our old inventory examples to make examples of
<#62469#><#11792#>extract1<#11792#><#62469#>'s input-output relationship. Unfortunately, it must
produce the empty inventory, for the three examples that we used above
because all prices are above one dollar. For a more interesting
input-output example, we need an inventory with more variety:
<#11797#>(cons<#11797#> <#11798#>(make-ir<#11798#> <#11799#>'<#11799#><#11800#>dagger<#11800#> <#11801#>.95)<#11801#>
<#11802#>(cons<#11802#> <#11803#>(make-ir<#11803#> <#11804#>'<#11804#><#11805#>Barbie<#11805#> <#11806#>17.95)<#11806#>
<#11807#>(cons<#11807#> <#11808#>(make-ir<#11808#> <#11809#>'<#11809#><#11810#>key-chain<#11810#> <#11811#>.55)<#11811#>
<#11812#>(cons<#11812#> <#11813#>(make-ir<#11813#> <#11814#>'<#11814#><#11815#>robot<#11815#> <#11816#>22.05)<#11816#>
<#11817#>empty))))<#11817#>
Out of the four items in this new inventory, two have prices below one
dollar. If given to <#62470#><#11821#>extract1<#11821#><#62470#>, we should get the result
<#11826#>(cons<#11826#> <#11827#>(make-ir<#11827#> <#11828#>'<#11828#><#11829#>dagger<#11829#> <#11830#>.95)<#11830#>
<#11831#>(cons<#11831#> <#11832#>(make-ir<#11832#> <#11833#>'<#11833#><#11834#>key-chain<#11834#> <#11835#>.55)<#11835#>
<#11836#>empty))<#11836#>
The new listing enumerates the items in the same order as the original, but
only contains those items whose prices match our condition.
The contract also implies that the template for <#62471#><#11840#>extract1<#11840#><#62471#> is identical
to that of <#62472#><#11841#>sum<#11841#><#62472#>, except for a name change:
<#11846#>(d<#11846#><#11847#>efine<#11847#> <#11848#>(extract1<#11848#> <#11849#>an-inv)<#11849#>
<#11850#>(c<#11850#><#11851#>ond<#11851#>
<#11852#>[<#11852#><#11853#>(empty?<#11853#> <#11854#>an-inv)<#11854#> <#11855#>...]<#11855#>
<#11856#>[<#11856#><#11857#>else<#11857#> <#11858#>...<#11858#> <#11859#>(first<#11859#> <#11860#>an-inv)<#11860#> <#11861#>...<#11861#> <#11862#>(extract1<#11862#> <#11863#>(rest<#11863#> <#11864#>an-inv))<#11864#> <#11865#>...]<#11865#><#11866#>))<#11866#>
As always, the difference in outputs between <#62473#><#11870#>sum<#11870#><#62473#> and
<#62474#><#11871#>extract1<#11871#><#62474#> does not affect the template derivation.
<#70991#>;; <#62475#><#11876#>extract1<#11876#> <#11877#>:<#11877#> <#11878#>inventory<#11878#> <#11879#><#11879#><#11880#>-;SPMgt;<#11880#><#11881#><#11881#> <#11882#>inventory<#11882#><#62475#><#70991#>
<#70992#>;; to create an <#62476#><#11883#>inventory<#11883#><#62476#> from <#62477#><#11884#>an-inv<#11884#><#62477#> for all<#70992#>
<#11885#>;; those items that cost less than $1<#11885#>
<#11886#>(d<#11886#><#11887#>efine<#11887#> <#11888#>(extract1<#11888#> <#11889#>an-inv)<#11889#>
<#11890#>(c<#11890#><#11891#>ond<#11891#>
<#11892#>[<#11892#><#11893#>(empty?<#11893#> <#11894#>an-inv)<#11894#> <#11895#>empty]<#11895#>
<#11896#>[<#11896#><#11897#>else<#11897#> <#11898#>(c<#11898#><#11899#>ond<#11899#>
<#11900#>[<#11900#><#11901#>(;SPMlt;=<#11901#> <#11902#>(ir-price<#11902#> <#11903#>(first<#11903#> <#11904#>an-inv))<#11904#> <#11905#>1.00)<#11905#>
<#11906#>(cons<#11906#> <#11907#>(first<#11907#> <#11908#>an-inv)<#11908#> <#11909#>(extract1<#11909#> <#11910#>(rest<#11910#> <#11911#>an-inv)))]<#11911#>
<#11912#>[<#11912#><#11913#>else<#11913#> <#11914#>(extract1<#11914#> <#11915#>(rest<#11915#> <#11916#>an-inv))]<#11916#><#11917#>)]<#11917#><#11918#>))<#11918#>
<#11922#>Figure: Extracting dollar items from an inventory<#11922#>
For the definition of the function body, we again analyze each case
separately. First, if <#62478#><#11924#>(empty?<#11924#>\ <#11925#>an-inv)<#11925#><#62478#> is true, then the answer is
clearly <#62479#><#11926#>empty<#11926#><#62479#>, because no item in an empty store costs less than
one dollar. Second, if the inventory is not empty, we first determine what
the expressions in the matching <#62480#><#11927#>cond<#11927#><#62480#>-clause compute. Since
<#62481#><#11928#>extract1<#11928#><#62481#> is the first recursive function to produce a list of
structures, let us look at our interesting example:
<#11933#>(cons<#11933#> <#11934#>(make-ir<#11934#> <#11935#>'<#11935#><#11936#>dagger<#11936#> <#11937#>.95)<#11937#>
<#11938#>(cons<#11938#> <#11939#>(make-ir<#11939#> <#11940#>'<#11940#><#11941#>Barbie<#11941#> <#11942#>17.95)<#11942#>
<#11943#>(cons<#11943#> <#11944#>(make-ir<#11944#> <#11945#>'<#11945#><#11946#>key-chain<#11946#> <#11947#>.55)<#11947#>
<#11948#>(cons<#11948#> <#11949#>(make-ir<#11949#> <#11950#>'<#11950#><#11951#>robot<#11951#> <#11952#>22.05)<#11952#>
<#11953#>empty))))<#11953#>
If <#62482#><#11957#>an-inv<#11957#><#62482#> stands for this inventory,
<#11962#>(first<#11962#> <#11963#>an-inv)<#11963#> <#11964#>=<#11964#> <#11965#>(make-ir<#11965#> <#11966#>'<#11966#><#11967#>dagger<#11967#> <#11968#>.95)<#11968#>
<#11969#>(rest<#11969#> <#11970#>an-inv)<#11970#> <#11971#>=<#11971#> <#11972#>(cons<#11972#> <#11973#>(make-ir<#11973#> <#11974#>'<#11974#><#11975#>Barbie<#11975#> <#11976#>17.95)<#11976#>
<#11977#>(cons<#11977#> <#11978#>(make-ir<#11978#> <#11979#>'<#11979#><#11980#>key-chain<#11980#> <#11981#>.55)<#11981#>
<#11982#>(c<#11982#><#11983#>ons<#11983#> <#11984#>(make-ir<#11984#> <#11985#>'<#11985#><#11986#>robot<#11986#> <#11987#>22.05)<#11987#>
<#11988#>empty)))<#11988#>
Assuming <#62483#><#11992#>extract1<#11992#><#62483#> works correctly, we also know that
<#11997#>(extract1<#11997#> <#11998#>(rest<#11998#> <#11999#>an-inv))<#11999#> <#12000#>=<#12000#> <#12001#>(c<#12001#><#12002#>ons<#12002#> <#12003#>(make-ir<#12003#> <#12004#>'<#12004#><#12005#>key-chain<#12005#> <#12006#>.55)<#12006#>
<#12007#>empty)<#12007#>
In other words, the recursive application of <#62484#><#12011#>extract1<#12011#><#62484#> produces the
appropriate selection from the rest of <#62485#><#12012#>an-inv<#12012#><#62485#>, which is a list
with a single inventory record.
To produce an appropriate inventory for all of <#62486#><#12013#>an-inv<#12013#><#62486#>, we must
decide what to do with the first item. Its price may be more or less than
one dollar, which suggest the following template for the second answer:
<#12018#>...<#12018#> <#12019#>(c<#12019#><#12020#>ond<#12020#>
<#12021#>[<#12021#><#12022#>(;SPMlt;=<#12022#> <#12023#>(ir-price<#12023#> <#12024#>(first<#12024#> <#12025#>an-inv))<#12025#> <#12026#>1.00)<#12026#> <#12027#>...]<#12027#>
<#12028#>[<#12028#><#12029#>else<#12029#> <#12030#>...]<#12030#><#12031#>)<#12031#> <#12032#>...<#12032#>
If the first item's price is one dollar or less, it must be included in the
final output and, according to our example, should be the first item on the
output. Translated into Scheme, the output should be a list whose first
item is <#62487#><#12036#>(first<#12036#>\ <#12037#>an-inv)<#12037#><#62487#> and whose rest is whatever the recursion
produces. If the price is more than one dollar, the item should not be
included. That is, the result should be whatever the recursion produces for
the <#62488#><#12038#>rest<#12038#><#62488#> of <#62489#><#12039#>an-inv<#12039#><#62489#> and nothing else. The complete
definition is displayed in figure~#figextract1#12040>.
<#12043#>Exercise 10.2.5<#12043#>
Define the function <#62490#><#12045#>extract;SPMgt;1<#12045#><#62490#>, which consumes an inventory and
creates an inventory from those records whose prices are above one
dollar.~ Solution<#62491#><#62491#>
<#12051#>Exercise 10.2.6<#12051#>
Develop a precise data definition for inventory1, which are inventory
listings of one-dollar stores. Using the new data definition, the contract
for <#62492#><#12053#>extract1<#12053#><#62492#> can be refined:
<#70993#>;; <#62493#><#12058#>extract1<#12058#> <#12059#>:<#12059#> <#12060#>inventory<#12060#> <#12061#><#12061#><#12062#>-;SPMgt;<#12062#><#12063#><#12063#> <#12064#>inventory1<#12064#><#62493#><#70993#>
<#12065#>(define<#12065#> <#12066#>(extract1<#12066#> <#12067#>an-inv)<#12067#> <#12068#>...)<#12068#>
Does the refined contract affect the development of the function above?
Solution<#62494#><#62494#>
<#12077#>Exercise 10.2.7<#12077#>
Develop the function <#62495#><#12079#>raise-prices<#12079#><#62495#>, which consumes an inventory and
produces an inventory in which all prices are raised by 5.
Solution<#62496#><#62496#>
<#12085#>Exercise 10.2.8<#12085#>
Adapt the function <#62497#><#12087#>recall<#12087#><#62497#> from exercise~#exrecall#12088> for the new
data definition of inventory. The function consumes the name of a toy
<#62498#><#12089#>ty<#12089#><#62498#> and an inventory and produces an inventory that contains all
items of the input with the exception of those labeled <#62499#><#12090#>ty<#12090#><#62499#>.
Solution<#62500#><#62500#>
<#12096#>Exercise 10.2.9<#12096#>
Adapt the function <#62501#><#12098#>name-robot<#12098#><#62501#> from exercise~#exsubst#12099> for the
new data definition of inventory. The function consumes an inventory and
produces an inventory with more accurate names. Specifically, it replaces
all occurrences of <#62502#><#12100#>'<#12100#><#12101#>robot<#12101#><#62502#> with <#62503#><#12102#>'<#12102#><#12103#>r2d3<#12103#><#62503#>.
Generalize <#62504#><#12104#>name-robot<#12104#><#62504#> to the function <#62505#><#12105#>substitute<#12105#><#62505#>. The new
function consumes two symbols, called <#62506#><#12106#>new<#12106#><#62506#> and <#62507#><#12107#>old<#12107#><#62507#>, and an
inventory. It produces a new inventory by substituting all occurrences of
<#62508#><#12108#>old<#12108#><#62508#> by <#62509#><#12109#>new<#12109#><#62509#> and leaving all others alone.
Solution<#62510#><#62510#>